Synchronization in complex systems with multiple time scales [Elektronische Ressource] / André Bergner. Betreuer: Jürgen Kurths

Synchronization incomplex systems withmultiple time scalesKumulative Dissertationzur Erlangung des akademischen GradesDoktor der Naturwissenschaften (Dr. rer. nat.)in der Wissenschaftsdisziplin Nichtlineare Dynamik / Datenanalyseeingereicht an derMathematisch-Naturwissenschaftlichen FakultätUniversität PotsdamvonAndré BergnerPotsdam, 18. August 2011 Published online at the Institutional Repository of the University of Potsdam: URL http://opus.kobv.de/ubp/volltexte/2011/5340/ URN urn:nbn:de:kobv:517-opus-53407 http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-53407 iAbstractIn the present work synchronization phenomena in complex dynamical systems exhibitingmultiple time scales have been analyzed. Multiple time scales can be active in differentmanners. Three different systems have been analyzed with different methods from dataanalysis.The first system studied is a large heterogenous network of bursting neurons, that isa system with two predominant time scales, the fast firing of action potentials (spikes)and the burst of repetitive spikes followed by a quiescent phase. This system has beenintegrated numerically and analyzed with methods based on recurrence in phase space.An interesting result are the different transitions to synchrony found in the two distincttime scales. Moreover, an anomalous synchronization effect can be observed in the fasttime scale, i.e.